To track the overall chat statistics (or by specific agent) and a customer satisfaction value, you need to go to the Reports section in the left-hand column, choose a period on the top left and the agent from the drop-down menu.
Here you can check a number of Total, New and Closed conversations for the selected period by clicking on each.
First response time and the Average conversation duration time is displayed on the top. In this case, the less is better, but mind that it fully depends whether you are closing conversations.
If you're seeing this report flat, most probably you forget to close conversations in time from the chat actions menu (read more).
See also: Customer satisfaction report